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Block #315,671

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2013, 3:17:48 PM Β· Difficulty 10.1127 Β· 6,488,266 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
daea4e9d080ed9546d35a89724f16ba39f03d8d465460f4391a4d96a120d4937
View on Chainz β†—

Height

#315,671

Difficulty

10.112652

Transactions

1

Size

206 B

Version

2

Bits

0a1cd6c5

Nonce

352,539

Timestamp

12/16/2013, 3:17:48 PM

Confirmations

6,488,266

Merkle Root

40fbadd3cee2f7ceca830f1dafd76bc5cc98285aed6e8debedc155d196c2241f
Transactions (1)
Coinbase40fbadd3cee2f7…c155d196c2241f
1 in β†’ 1 out9.7600 XPM116 B
AbwWkWZt…kawDhufa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.632 Γ— 10⁹⁡(96-digit number)
16324079836417792519…85098793974037372160
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.632 Γ— 10⁹⁡(96-digit number)
16324079836417792519…85098793974037372159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.632 Γ— 10⁹⁡(96-digit number)
16324079836417792519…85098793974037372161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.264 Γ— 10⁹⁡(96-digit number)
32648159672835585039…70197587948074744319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.264 Γ— 10⁹⁡(96-digit number)
32648159672835585039…70197587948074744321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.529 Γ— 10⁹⁡(96-digit number)
65296319345671170078…40395175896149488639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.529 Γ— 10⁹⁡(96-digit number)
65296319345671170078…40395175896149488641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁢(97-digit number)
13059263869134234015…80790351792298977279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.305 Γ— 10⁹⁢(97-digit number)
13059263869134234015…80790351792298977281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.611 Γ— 10⁹⁢(97-digit number)
26118527738268468031…61580703584597954559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.611 Γ— 10⁹⁢(97-digit number)
26118527738268468031…61580703584597954561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 315671

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock daea4e9d080ed9546d35a89724f16ba39f03d8d465460f4391a4d96a120d4937

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #315,671 on Chainz β†—
Circulating Supply:57,675,546 XPMΒ·at block #6,803,936 Β· updates every 60s
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